The area of a rectangle is represented by the function x3 − 2×2 − 40x − 64. The width of the rectangle is x + 4. Find the expression represe

Question

The area of a rectangle is represented by the function x3 − 2×2 − 40x − 64. The width of the rectangle is x + 4. Find the expression representing the length of the rectangle.

A. x2 − 8x − 20
B. x2 + 12x + 20
C. x2 − 6x − 16
D. x2 + 10x + 16

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Ivy 2 weeks 2021-09-11T17:14:51+00:00 1 Answer 0

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    2021-09-11T17:16:12+00:00

    Answer:

    Step-by-step explanation:

    If the area is

    x^3-2x^2-40x-64

    and area = length * width and our width is given as x + 4, then the length is found by dividing the area by the width.  You could do that using long division, but it’s easier using synthetic division.

    -4 |   1   -2   -40   -64

        ______________

           1

    This is how you start.  The -4 inside the box comes from the factor you are dividing by.  If x + 4 = 0, then x = -4.  The numbers after are the coefficients from each descending power of x.  Multiply the -4 by the 1 and put that product up under the -2 and add to get:

    -4 |   1   -2   -40   -64

                -4

    ——————————–

           1     -6

    Now multiply -4 by -6 and put that product up under the -40 and add:

    -4 |  1    -2  -40   -64

               -4   24

       ————————-

          1    -6    -16

    Multiplying -4 by -16 gives you 64 so when you add you get a remainder of 0.

    The numbers under the line give you the depressed polynomial

    x^2-6x-16

    That gives you the expression for the length.  That’s C.        

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